Finite Group Databasebeta

← Group #72342688

Character table — Group #72342688

Order 1536.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size1111111122226666666666666666666666661212121212121212242424242424242424242424242424242424242424242424242424242424242432323232323232323232323232323232
order12448888248822222244444488888888888822448888224444444444444488888888888888883666121212122424242424242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ311111111-1-1-1-1-1-1-1111-1-1-1111111111-1-1-1-1-1-11-11-111-1-11-11-1111111-1-1-1-1-1-111-1-1111111-1-1-1-1-1-11-1-11-1-1111111-1-1-1-1
χ411111111-1-1-1-1-1-1-1111-1-1-1111111111-1-1-1-1-1-11-11-111-1-1-11-11-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111111-1-11-1-1111111-1-1-1-1
χ51111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-111111111-1-1-1-1-1-1-1-1
χ61111-1-1-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ71111-1-1-1-1-1-111-1-1-1111-1-1-1111-1-1-1-1-1-11111111-11-1-1-1111-11-111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-1111-1-11-1-111-1-1-1-11111
χ81111-1-1-1-1-1-111-1-1-1111-1-1-1111-1-1-1-1-1-11111111-11-1-1-111-11-11-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-11-1-11-1-111-1-1-1-11111
χ911-1-1ii−i−i1-1i−i1-1-11-1-111-111-1iii−i−i−iiii−i−i−i11-1-1i−ii−i1-1-111-1ii−i−i1-1ii−i−ii−ii−i11-1-1i−i11-1-1i−i1111-1-1-1-1ii−i−iii−i−i
χ1011-1-1ii−i−i1-1i−i1-1-11-1-111-111-1iii−i−i−iiii−i−i−i11-1-1i−ii−i-111-1-11−i−iii-11−i−iii−ii−ii-1-111−ii-1-111−ii1111-1-1-1-1ii−i−iii−i−i
χ1111-1-1ii−i−i-11−ii-1111-1-1-1-1111-1iii−i−i−i−i−i−iiii1-1-11i−i−ii11-1-11-1ii−i−i-11−i−iiii−i−ii11-1-1i−i-1-111−ii1-1-1111-1-1ii−i−i−i−iii
χ1211-1-1ii−i−i-11−ii-1111-1-1-1-1111-1iii−i−i−i−i−i−iiii1-1-11i−i−ii-1-111-11−i−iii1-1ii−i−i−iii−i-1-111−ii11-1-1i−i1-1-1111-1-1ii−i−i−i−iii
χ1311-1-1−i−iii1-1−ii1-1-11-1-111-111-1−i−i−iiii−i−i−iiii11-1-1−ii−ii1-1-111-1−i−iii1-1−i−iii−ii−ii11-1-1−ii11-1-1−ii1111-1-1-1-1−i−iii−i−iii
χ1411-1-1−i−iii1-1−ii1-1-11-1-111-111-1−i−i−iiii−i−i−iiii11-1-1−ii−ii-111-1-11ii−i−i-11ii−i−ii−ii−i-1-111i−i-1-111i−i1111-1-1-1-1−i−iii−i−iii
χ1511-1-1−i−iii-11i−i-1111-1-1-1-1111-1−i−i−iiiiiii−i−i−i1-1-11−iii−i11-1-11-1−i−iii-11ii−i−i−iii−i11-1-1−ii-1-111i−i1-1-1111-1-1−i−iiiii−i−i
χ1611-1-1−i−iii-11i−i-1111-1-1-1-1111-1−i−i−iiiiiii−i−i−i1-1-11−iii−i-1-111-11ii−i−i1-1−i−iiii−i−ii-1-111i−i11-1-1−ii1-1-1111-1-1−i−iiiii−i−i
χ172222222222222222222222222222222222222222222200000000000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ1822222222-2-2-2-2-2-2-2222-2-2-2222222222-2-2-2-2-2-22-22-222-2-200000000000000000000000000000000-111-111-1-1-1-1-1-11111
χ192222-2-2-2-222-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000-1-1-1-1-1-1-1-111111111
χ202222-2-2-2-2-2-222-2-2-2222-2-2-2222-2-2-2-2-2-22222222-22-2-2-22200000000000000000000000000000000-111-111-1-11111-1-1-1-1
χ2122-2-22i2i−2i−2i2-22i−2i2-2-22-2-222-222-22i2i2i−2i−2i−2i2i2i2i−2i−2i−2i22-2-22i−2i2i−2i00000000000000000000000000000000-1-1-1-11111−i−iii−i−iii
χ2222-2-22i2i−2i−2i-22−2i2i-2222-2-2-2-2222-22i2i2i−2i−2i−2i−2i−2i−2i2i2i2i2-2-222i−2i−2i2i00000000000000000000000000000000-111-1-1-111−i−iiiii−i−i
χ2322-2-2−2i−2i2i2i2-2−2i2i2-2-22-2-222-222-2−2i−2i−2i2i2i2i−2i−2i−2i2i2i2i22-2-2−2i2i−2i2i00000000000000000000000000000000-1-1-1-11111ii−i−iii−i−i
χ2422-2-2−2i−2i2i2i-222i−2i-2222-2-2-2-2222-2−2i−2i−2i2i2i2i2i2i2i−2i−2i−2i2-2-22−2i2i2i−2i00000000000000000000000000000000-111-1-1-111ii−i−i−i−iii
χ253333333333333-1-13-1-1-1-13-1-133-1-13-1-13-1-13-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1110000000000000000
χ263333333333333-1-13-1-1-1-13-1-133-1-13-1-13-1-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-11111-1-10000000000000000
χ27333333333333-13-1-13-13-1-13-1-1-13-1-13-1-13-1-13-1-1-1-1-1-1-1-1-11111-1-11-11-1-1-11-11-111111-11-1-1-11-11-1-1-10000000000000000
χ28333333333333-13-1-13-13-1-13-1-1-13-1-13-1-13-1-13-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1111-11-11-1-1-1-1-11-1111-11-11110000000000000000
χ29333333333333-1-13-1-13-13-1-13-1-1-13-1-13-1-13-1-13-1-1-1-1-1-1-1-11111-1-1-11-11-1-1-11-111111-11-11-1-1-11-11-1-10000000000000000
χ30333333333333-1-13-1-13-13-1-13-1-1-13-1-13-1-13-1-13-1-1-1-1-1-1-1-1-1-1-1-1111-11-1111-11-1-1-1-1-11-11-1111-11-1110000000000000000
χ3133333333-3-3-3-311-3-1-131-31-13-1-1-13-1-1311-311-3-11-11-1-1111-11-1-1-1-11-11111-11-111-1-1-11-11-1-11-11-1110000000000000000
χ3233333333-3-3-3-311-3-1-131-31-13-1-1-13-1-1311-311-3-11-11-1-111-11-11111-11-1-1-1-11-11-1-1111-11-111-11-11-1-10000000000000000
χ3333333333-3-3-3-31-31-13-1-3113-1-1-13-1-13-11-311-31-11-11-1-1111-11-1-1-11-11-111-11-1111-1-11-11-1-1-1-11-11110000000000000000
χ3433333333-3-3-3-31-31-13-1-3113-1-1-13-1-13-11-311-31-11-11-1-111-11-1111-11-11-1-11-11-1-1-111-11-11111-11-1-1-10000000000000000
χ3533333333-3-3-3-3-3113-1-111-3-1-133-1-13-1-1-311-311-11-11-1-1111-11-111-1-1-1-1-1-1111111-1-1-1-1-1-1111111-1-10000000000000000
χ3633333333-3-3-3-3-3113-1-111-3-1-133-1-13-1-1-311-311-11-11-1-111-11-11-1-1111111-1-1-1-1-1-1111111-1-1-1-1-1-1110000000000000000
χ373333-3-3-3-333-3-33-1-13-1-1-1-13-1-13-311-311-311-311-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ383333-3-3-3-333-3-33-1-13-1-1-1-13-1-13-311-311-311-311-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111110000000000000000
χ393333-3-3-3-333-3-3-13-1-13-13-1-13-1-11-311-311-311-31-1-1-1-111111111-1-1-11-11-1-1-11-11-1-1-1-11-11-1111-11-1110000000000000000
χ403333-3-3-3-333-3-3-13-1-13-13-1-13-1-11-311-311-311-31-1-1-1-11111-1-1-1-1111-11-1111-11-11111-11-11-1-1-11-11-1-10000000000000000
χ413333-3-3-3-333-3-3-1-13-1-13-13-1-13-111-311-311-311-3-1-1-1-111111111-1-11-11-1-1-11-11-1-1-1-1-1-11-1111-11-11110000000000000000
χ423333-3-3-3-333-3-3-1-13-1-13-13-1-13-111-311-311-311-3-1-1-1-11111-1-1-1-111-11-1111-11-1111111-11-1-1-11-11-1-1-10000000000000000
χ433333-3-3-3-3-3-33311-3-1-131-31-13-111-311-3-1-13-1-13-11-1111-1-11-11-1-1-11-11-111-11-11-1-111-11-11111-11-1-1-10000000000000000
χ443333-3-3-3-3-3-33311-3-1-131-31-13-111-311-3-1-13-1-13-11-1111-1-1-11-1111-11-11-1-11-11-111-1-11-11-1-1-1-11-11110000000000000000
χ453333-3-3-3-3-3-3331-31-13-1-3113-1-11-311-31-13-1-13-1-11-1111-1-11-11-1-1-1-11-11111-11-1-1-1111-11-111-11-11-1-10000000000000000
χ463333-3-3-3-3-3-3331-31-13-1-3113-1-11-311-31-13-1-13-1-11-1111-1-1-11-11111-11-1-1-1-11-1111-1-1-11-11-1-11-11-1110000000000000000
χ473333-3-3-3-3-3-333-3113-1-111-3-1-13-311-3113-1-13-1-1-11-1111-1-11-11-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111110000000000000000
χ483333-3-3-3-3-3-333-3113-1-111-3-1-13-311-3113-1-13-1-1-11-1111-1-1-11-11-1-1-1-1-1-111111111-1-1111111-1-1-1-1-1-10000000000000000
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χ5133-3-33i3i−3i−3i3-33i−3i-11-3-11-3-131-131−i−i3iii−3i−i−i3iii−3i-1-111−ii−ii1-1-11-11−iii−i-11−iii−ii−ii−i-111-1−ii-111-1−ii0000000000000000
χ5233-3-33i3i−3i−3i3-33i−3i-11-3-11-3-131-131−i−i3iii−3i−i−i3iii−3i-1-111−ii−ii-111-11-1i−i−ii1-1i−i−ii−ii−ii1-1-11i−i1-1-11i−i0000000000000000
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χ858-88i−8i−8ζ7−8ζ238ζ7+8ζ238ζ5+8ζ13−8ζ5−8ζ1300000000000000000000000000000000000000000000000000000000000000000000-1−i3i313−3−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13
χ868-88i−8i−8ζ7−8ζ238ζ7+8ζ238ζ5+8ζ13−8ζ5−8ζ1300000000000000000000000000000000000000000000000000000000000000000000-1i3−i31−33−iiζ7+ζ23−ζ7−ζ23−ζ5−ζ13ζ5+ζ13−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13
χ878-8−8i8i−8ζ5−8ζ138ζ5+8ζ138ζ7+8ζ23−8ζ7−8ζ2300000000000000000000000000000000000000000000000000000000000000000000200-200−2i2i−2ζ5−2ζ132ζ5+2ζ132ζ7+2ζ23−2ζ7−2ζ230000
χ888-8−8i8i−8ζ5−8ζ138ζ5+8ζ138ζ7+8ζ23−8ζ7−8ζ2300000000000000000000000000000000000000000000000000000000000000000000-1−i3i31−33i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23
χ898-8−8i8i−8ζ5−8ζ138ζ5+8ζ138ζ7+8ζ23−8ζ7−8ζ2300000000000000000000000000000000000000000000000000000000000000000000-1i3−i313−3i−iζ5+ζ13−ζ5−ζ13−ζ7−ζ23ζ7+ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23
χ908-8−8i8i8ζ5+8ζ13−8ζ5−8ζ13−8ζ7−8ζ238ζ7+8ζ2300000000000000000000000000000000000000000000000000000000000000000000200-200−2i2i2ζ5+2ζ13−2ζ5−2ζ13−2ζ7−2ζ232ζ7+2ζ230000
χ918-8−8i8i8ζ5+8ζ13−8ζ5−8ζ13−8ζ7−8ζ238ζ7+8ζ2300000000000000000000000000000000000000000000000000000000000000000000-1−i3i31−33i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23
χ928-8−8i8i8ζ5+8ζ13−8ζ5−8ζ13−8ζ7−8ζ238ζ7+8ζ2300000000000000000000000000000000000000000000000000000000000000000000-1i3−i313−3i−i−ζ5−ζ13ζ5+ζ13ζ7+ζ23−ζ7−ζ23−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.